Sometimes I need to get some files from my desktop computer, so I send a wake on LAN package (using my laptop) to the computer and it turns on. But every 30 times I have to wait ~30 minutes for the file system check (and I can't cancel it through SSH or so).

Many people would like to move the file system check to shutdown, but these projects and ideas seem to be quite abandoned:

Basically, you can prompt the user (or just go ahead and do AutoFsck without prompting) on lightdm shutdown. The bottom line is block shutdown with a small init.d script that checks for a flag (i.e. file or contents of a file, like number of reboots) that is set and removed by your AutoFsck calling script. This way AutoFsck will definitely start and finish and the system will only shutdown once AutoFsck finishes. With this script tandem, you can disable automatic file system checks in tune2fs because you implemented 'automatic' AutoFsck via lightdm or any other process you choose.